By Erica Klarreich FOR millennia, jugglers have relied on timing, precision and sheer chutzpah to see them through as they toss flaming torches, chainsaws and raw eggs before dazzled audiences. But these days there is a tool in their bag of tricks that you won’t see on stage – a little mathematics. Over the past two decades, enthusiasts have developed a theory of juggling that has allowed them to invent many different new ways to juggle. And not content with that, they are now even exploring what happens when jugglers throw not in patterns, but randomly – and the results are mind-boggling. Juggling maths took off in 1985, when several mathematically inclined jugglers came up with a notation for juggling patterns, called “site swap notation”. Until then, jugglers had shared new tricks by demonstration, but site swap notation made it possible to write down a trick, even one that had yet to be performed, and send it to a friend. “It’s like musical notation,” says Gregory Warrington, a juggler and a mathematics professor at the University of Massachusetts in Amherst. “If you hear someone play a tune, you can try to copy it just by listening, but if you both know how to read music,